A case of the Jacobian conjecture
type: Item
instance of: scholarly article
title: A case of the Jacobian conjecture
zbMATH Open document ID: 0811.13013
DOI: 10.1016/0022-4049(94)90082-5
author: Charles Ching-An Cheng
author: Takis Sakkalis
author: Stuart Sui-Sheng Wang
published in: Journal of Pure and Applied Algebra
publication date: 1995-05-07T00:00:00Z
review text: An elementary proof for the following known theorem concerning the Jacobian conjecture is given: Let \(F = (F_ 1, \dots, F_ n) : \mathbb{C}^ n \to \mathbb{C}^ n\) be a polynomial map, \(F_ i = X_ i + H_ i\), \(H_ 1, \dots, H_ n\) homogeneous polynomials in \(\mathbb{C} [X_ 1, \dots, X_ n]\) of degree \(d \geq 2\) and \(J(H)^ 2 = 0\), \(J(H)\) the jacobian matrix of \(H = (H_ 1, \dots, H_ n)\). Then \(F\) has a polynomial \(G\) inverse namely, \(G = (X_ 1 - H_ 1, \dots, X_ n - H_ n)\).
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 681822
zbMATH Keywords: Jacobian conjecture
Wikidata QID: Q122964218
reviewed by: Gerhard Pfister
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90082-5
OpenAlex ID: W2035289184
cites work: The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
cites work: Subgroups of polynomial automorphisms
cites work: Q3970317
cites work: Power-exact, nilpotent, homogeneous matrices
cites work: A case of the Jacobian Conjecture
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description: scientific article; zbMATH DE number 681822